Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊#14546095 |
| unambiguous semidirect product | (C2×C5)⋊#14546095 |
| derived, Hall | C5×C112⋊C9 ⋊ C22 |
| Hall | C112⋊C9 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ C2×D45 |
| Sylow | C5 ⋊ C2×#14546095 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#14546095 |
| commutator, cosocle, hypocenter | C5×C112⋊C9 | C22 |
| Frattini | C3 | C2×C5⋊#10624391 |
| Fitting, socle | C2×C3×C5×C112 | D3 |
| LCS | G ▷ C5×C112⋊C9 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
678 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 256);